In general, the principle of relativity is the requirement that the laws of physics be the same for all observers. Somewhat more particularly, the measurements an observer makes in his frame of reference of an important event are related in a particular way to those made by another observer. Several principles of "relativity" have been developed, starting with the Galilean version.
Galileo and others considered only inertial reference frames (see the discussion of such frames in frame of reference) in uniform translation relative to each other. The measurement of time was assumed to be the same for all observers, but the measurements of distance made by an observer differ from those by another depending on the relative velocity between the observers' frames of reference. The measurements made by one can be transformed to those by another one. Such a transformation is called the Galilean transformation.
Einstein saw, however, that if the vacuum speed of light was really the ultimate velocity in our physical world, a different kind of transformation was called for. If information about an important event cannot reach us faster than light (or any form of electromagnetic phenomenon) can, the Galilean assumption of universal time has to be discarded. The transformation of an observer's measurements to another observer's measurements, now changed, is called the Lorentz transformation. For details, seetheory of relativity and special relativity.
General relativity extended the principle of relativity to accelerated frames of reference in a gravity field.
So the principle of Galileanrelativity could be stated as: "The laws of nature are the same in all inertial frames," where the laws of nature were understood to be Newton's laws of motion and any laws based on them.
Galilean transformations apply a principle that is based on Newton's first law: Any frame of reference that is moving at a constant velocity relative to an inertial frame is also an inertial frame.
The speed of light relative to the lab would therefore be different for light rays moving in different directions relative to the lab.
Historically, the first principle of relativity that was formulated was a principle of relativity of uniform motion suggested by the observation that there doesn't seem to be a phenomenon in dynamics that will allow an observer to establish a zero point of velocity, nor a preferred direction.
In Galileanrelativity, reference frames are related to each other in an intuitive way: to transform the velocity of an object from one frame to another, the vector representing the velocity of the object is added to the vector representing the velocity difference between the two reference frames.
General relativity is a theory of gravitation that describes the properties of the mediator of gravitational interaction, in general relativity the mediator of gravitational interaction is deformation of space-time geometry.
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